{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:C2IRIW65D3PV5WGS4O5LZAMIVP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3393262a2c05991314362b8c9c2c0bb18d23c69d083a35a2d1619e5b20417b4b","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"1998-10-26T00:00:00Z","title_canon_sha256":"d21ac1f67ee56b5295efea827cd1103424e6bfb240fd8c997a15af5770bb98c0"},"schema_version":"1.0","source":{"id":"math/9810190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9810190","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/9810190v1","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9810190","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"C2IRIW65D3PV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"C2IRIW65D3PV5WGS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"C2IRIW65","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:a4fbfa2aaa088a673e80c13e99f36d7bb515dd686961be74fb3c9b20086c850a","target":"graph","created_at":"2026-05-18T01:05:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The history, definition and principal properties of automatic groups and their generalisations to subgroups and cosets are reviewed briefly, mainly from a computational perspective. A result about the asynchronous automaticity of an HNN extension is then proved and applied to an example that was proposed by Mark Sapir.","authors_text":"Derek F. Holt","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"1998-10-26T00:00:00Z","title":"Automatic groups, subgroups and cosets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9810190","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f3003bef2088c866617e38974400bbcba265523e5e152c096c4568a488c18d4d","target":"record","created_at":"2026-05-18T01:05:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3393262a2c05991314362b8c9c2c0bb18d23c69d083a35a2d1619e5b20417b4b","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"1998-10-26T00:00:00Z","title_canon_sha256":"d21ac1f67ee56b5295efea827cd1103424e6bfb240fd8c997a15af5770bb98c0"},"schema_version":"1.0","source":{"id":"math/9810190","kind":"arxiv","version":1}},"canonical_sha256":"1691145bdd1edf5ed8d2e3babc8188abd74ecf264c3d62468c9c59ae5fc2d85e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1691145bdd1edf5ed8d2e3babc8188abd74ecf264c3d62468c9c59ae5fc2d85e","first_computed_at":"2026-05-18T01:05:33.599101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:33.599101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k3PJ7puBKu7q2IRoNCL+32iSzDzk4JJG1+QshgWA8RsgVrzfKZi9YqfQxbDJjoGdHmEvGKTEHzDnYmTfMBybBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:33.599719Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9810190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3003bef2088c866617e38974400bbcba265523e5e152c096c4568a488c18d4d","sha256:a4fbfa2aaa088a673e80c13e99f36d7bb515dd686961be74fb3c9b20086c850a"],"state_sha256":"16b3b8d3399c7e73be1cefc3025135690754e17c0ccb304e8dadb4b6565312f9"}